1. 3.7 Graphs of Rational Functions
Definition: A rational function is a ratio of two polynomials, providing that the polynomial in the denominator is not the zero polynomial.
Examples:
An example that is not a rational function is

2. Finding the domain of a rational function
The domain of a polynomial function is the set of all real numbers {x|(-∞ <x<∞)}.
The domain of a rational function is restricted to real numbers that do not cause the denominator to equal zero.

3. Example 1: Find the domain of
Set the denominator equal to zero and solve for x
The domain is (-∞, -7)U(-7, ∞)

4. Example 2: Find the domain of
Set the denominator equal to zero and solve for x
X=0
The domain is

5. Example 3 Find the domain of f(x)=
Set the denominator equal to zero and solve for x.
Factor: (x+3)(x+2)=0
Set each factor equal to zero and solve for x
The domain is (-∞,-3)U(-3,-2)U(-2,∞)

6. Example 4 Find the domain of f(x)=
Set the denominator equal to zero and solve for x.
Factor: (x-2)(x+1). Observe that (x-2) is a factor in the numerator. Do not re-write the equation as f(x)=
Set each factor equal to zero and solve for x
x-2=0, x=2 x+1=0, x=-1
The domain is (-∞,-1)U(-1, 2)U(2,∞)

7. Example 5 Find the domain of
Set the denominator equal to zero and solve for x
does not factor

8. Use Quadratic Formula

11. And the domain is

12. Hw: